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Home » Solution:** The average of the three expressions is given by: - Silent Sales Machine

Solution:** The average of the three expressions is given by: - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 The lateral surface area of a cone is given by:

📌 where $ r = 2x $ and $ l = 5x $. Substituting:

📌 A = \pi (2x)(5x) = 10\pi x^2

📌 \boxed{10\pi x^2}

📌 Question: A quantum algorithm designer is modeling a 3D lattice where each node is a cube of side $ x $. A diagonal connects two opposite vertices of the cube. What is the length of this space diagonal in terms of $ x $?

📌 The space diagonal $ d $ of a cube with side length $ x $ is given by the 3D Pythagorean theorem:

📌 d = \sqrt{x^2 + x^2 + x^2} = \sqrt{3x^2} = x\sqrt{3}

📌 \boxed{x\sqrt{3}}

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